For the first question, I would say no because the weights are not 'symmetrical' about the mean.
I would have said it is symmetrical if it was:
The mean is 10.04 g to the 2nd decimal place. And I'm getting the standard deviation as 0.182 instead of 0.32...
But looking at the shape of distribution, I would say it is fair ecause it is negatively skewed (it is 'pushed' towards the right a little more).